= Latent heat from a vapor-pressure slope
{title2=$L_m\simeq-R\,d\ln(p/p_*)/d(1/T)$}
Within the <Ideal-vapor Clausius-Clapeyron approximation>, a local slope of the <natural logarithm> of <saturation pressure> against <inverse temperature> estimates the molar <latent heat>:
$$
L_m(T)\simeq-R\frac{d\ln(p/p_*)}{d(1/T)}.
$$
In the <stipulated vapor-pressure calculation>, the slope is $-4811.16\,\mathrm K$, which recovers $40.0\,\mathrm{kJ\,mol^{-1}}$. For variable $L_m(T)$, a two-point estimate gives an average weighted by $T^{-2}$, rather than the <latent heat> at an arbitrary midpoint. Differentiating noisy <pressure> measurements amplifies their errors. Outside the ideal-vapor regime, use independently determined <molar volumes> in $L_m=T\Delta v_m\,dp/dT$; a straight-looking graph alone cannot establish that the <gas> is ideal.
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